2 problems

Let $A_t$ denote the spherical averaging operator, let $\partial_t^\gamma$ be the fractional time derivative, and let $L^p_s(\mathbb{R}^d)$ denote the inhomogeneous Sobolev space.…

Let $E\subset [1,2]$ satisfy $\dim_M E=\dim_A E=\beta$. For each scale $j$, let $\mathcal{Z}_j(E)$ index a minimal collection of $\delta$-separated points $t_\nu$ whose intervals…